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Two identical coils A and B have 400 turns placed such that 60% of flux produced by one coil links with the other. If a current of 10A flowing in coil A produces a flux of 20 mWb in it, find the mutual inductance between coil A and B.
480 H
10 H
100 H
0.48 H
0.48 H
Mutual inductance is defined by the flux linkage of one coil due to the current in another. Here, the mutual flux linkage is calculated as 60% of the total flux produced by coil A, which is then linked with all 400 turns of coil B.
IS 1885-32 (Electrotechnical Vocabulary: Magnetic Circuits)
Mutual inductance is defined by the flux linkage of one coil due to the current in another. Here, the mutual flux linkage is calculated as 60% of the total flux produced by coil A, which is then linked with all 400 turns of coil B.
M=IAтАЛNBтАЛ╬жMтАЛтАЛ тАФ Basic definition of mutual inductance
╬жMтАЛ=k╬жAтАЛ тАФ Mutual flux calculation
When a current IAтАЛ flows through coil A, it creates a total flux ╬жAтАЛ. The mutual flux ╬жMтАЛ linking coil B is k├Ч╬жAтАЛ, where k is the coupling coefficient. The mutual inductance M is defined as M=IAтАЛNBтАЛ╬жMтАЛтАЛ.
Given NAтАЛ=NBтАЛ=400 turns.
Flux in A, ╬жAтАЛ=20┬аmWb=20├Ч10тИТ3┬аWb.
Coupling coefficient k=0.60.
Mutual flux ╬жMтАЛ=0.60├Ч20├Ч10тИТ3=12├Ч10тИТ3┬аWb.
Mutual inductance M=10400├Ч12├Ч10тИТ3тАЛ=0.48┬аH.
Fundamental principle for transformer operation
Allows voltage transformation without physical contact
Dependent on magnetic coupling coefficient
Sensitive to core material properties
Transformers
Induction motors
Coupled circuits
The coupling coefficient k represents the fraction of flux linking the second coil.
Option B (10 H) is often obtained by ignoring the 60% linkage factor, assuming k=1 and miscalculating.
The result M=0.48┬аH is physically significant as it reflects partial magnetic linkage.
D is correct тАФ The mutual inductance is calculated as M=0.48┬аH based on the 60% flux linkage coefficient.
Always verify if the coupling coefficient k is 1 (perfect coupling) or less, as it directly scales the mutual inductance M in non-ideal magnetic circuits.
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